where \(c_{+} = \max (c,0)\)  and where \(\sigma _u > 0\)  and \(\xi \in \mathbb {R}\)  denote the scale and shape parameters respectively. The shape parameter is invariant to the choice of threshold but the scale parameter is threshold-dependent. The threshold \(u\)  is typically determined using some standard selection diagnostics [1]} such as ensuring that the parameters are stable with respect to the threshold for all threshold choices larger than \(u\) .
